Projectile from Height

From height h with initial velocity (v₀ₓ, v₀ᵧ), time of flight: T = (v₀ᵧ + √(v₀ᵧ² + 2gh))/g.

Range R = v₀ₓ · T.

Impact speed: v = √(v₀ₓ² + v₀ᵧ² + 2gh) (from energy conservation).

The trajectory is asymmetric — ascent time ≠ descent time.